Last updated: July 31, 2026
Isosceles Triangle Find A Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
a=2×√(b^2-h^2)
Where:
- a=base length
- b=equal leg length
- h=height to base
Worked Examples
Recover base 6
Equal legs 5 and height 4 produce a base of 6.
- 1a=2×√(25-16)
- 2a=2×3=6
Recover base 10
Equal legs 13 and height 12 produce a base of 10.
- 1a=2×√(169-144)
- 2a=2×5=10
Decimal example
This relation also works with non-integer triangles.
- 1a=2×√(7.5²-6²)
- 2Round the result to six decimals
Invalid height
The equal leg must be longer than the height.
- 1Check b>h
- 25 is not greater than 5, so the base cannot be recovered as a real value.
Introduction
This isosceles triangle find-a calculator solves for the base when you know the equal legs and the height. The formula comes from splitting the triangle into two right triangles, then doubling the half-base. It is especially helpful when a problem labels the base as a and the equal sides as b.
What this calculator means by a
In this calculator, a is the base and b is the equal side length. That naming is the reverse of some textbooks, so it helps to confirm the labels before entering values.
a is the base output
b is each equal leg input
h is the altitude from apex to base
Where the formula comes from
The altitude splits the base into two equal halves. Each half-base forms a right triangle with hypotenuse b and leg h.
(a/2)²=b²-h²
a/2=√(b²-h²)
Double the half-base to get a
This is the same geometry behind the full isosceles triangle calculator.
Input guide
Enter the equal leg length and the height using the same unit. The result for the base will be in that same linear unit.
- 1
Use positive lengths
- 2
Decimals are allowed
- 3
Keep both inputs in the same measurement system
Validation rules
The equal leg must be strictly greater than the height. Otherwise the square-root term is zero or negative for this calculator.
b must be finite
h must be finite
b>0 and h>0
b>h
If b=h, the half-base becomes zero and the triangle degenerates.
Manual verification
After computing the base, you can halve it and check that h²+(a/2)² equals b².
Solve for a
Compute a/2
Use the Pythagorean theorem
Confirm the original leg value
Practical uses
This calculation appears in geometry exercises, framing layouts, and any symmetric design where the altitude is measured directly.
Reverse-engineering a base span
Checking symmetric supports
Construction sketches
Education and tutoring
FAQs
What does this find-a calculator return?
It returns the base length a from the equal leg b and the height h.
Why is the output called a?
This calculator follows a naming convention where a is the base and b represents the equal legs.
Why must the equal leg be greater than the height?
Because the formula uses √(b²-h²). If b is not larger than h, the square root does not represent a positive half-base.
Can I use decimals?
Yes. Decimal inputs are accepted and the output is rounded to 6 decimal places.
Does this calculator also find area?
No. This version focuses on recovering the base length only.
How can I check the result?
Take half the computed base and confirm that h²+(a/2)² equals b².